An Exact Method to Enumerate Decomposition Charts for Index Generation Functions

Abstract

In a previous paper, the balls-in-bins model was shown to efficiently enumerate random functions as a means to estimate the size of programmable architecture for the circuit needed to realize an index generation function. Because there are so many balls-in-bins instances, it is typically not possible to enumerate all. So, a Monte Carlo simulation is performed instead. In this paper, we show how to improve the balls-in-bins estimates by using a weighted approach. An exact enumeration approach is also proposed that allows for the exhaustive enumeration of decomposition charts for the same analysis as in a previous paper. It is based on the enumeration of integer partitions.